OK, let's crack this. We're given 378 and our task is to multiply it by 35. Essentially, we'll be adding 378 to itself 35 times.
Step 1: 0 + 378 = 378
Step 2: 378 + 378 = 756
Step 3: 756 + 378 = 1134
Step 4: 1134 + 378 = 1512
Step 5: 1512 + 378 = 1890
Step 6: 1890 + 378 = 2268
Step 7: 2268 + 378 = 2646
Step 8: 2646 + 378 = 3024
Step 9: 3024 + 378 = 3402
Step 10: 3402 + 378 = 3780
Step 11: 3780 + 378 = 4158
Step 12: 4158 + 378 = 4536
Step 13: 4536 + 378 = 4914
Step 14: 4914 + 378 = 5292
Step 15: 5292 + 378 = 5670
Step 16: 5670 + 378 = 6048
Step 17: 6048 + 378 = 6426
Step 18: 6426 + 378 = 6804
Step 19: 6804 + 378 = 7182
Step 20: 7182 + 378 = 7560
Step 21: 7560 + 378 = 7938
Step 22: 7938 + 378 = 8316
Step 23: 8316 + 378 = 8694
Step 24: 8694 + 378 = 9072
Step 25: 9072 + 378 = 9450
Step 26: 9450 + 378 = 9828
Step 27: 9828 + 378 = 10206
Step 28: 10206 + 378 = 10584
Step 29: 10584 + 378 = 10962
Step 30: 10962 + 378 = 11340
Step 31: 11340 + 378 = 11718
Step 32: 11718 + 378 = 12096
Step 33: 12096 + 378 = 12474
Step 34: 12474 + 378 = 12852
Step 35: 12852 + 378 = 13230

So, 378*35 = 13230